R is in Third Normal Form (3NF) with respect to F (or simply in 3NF whenever F is understood from context) if, for every nontrivial FD, X [right arrow] A [element of] F, either X is a superkey for R or A is prime.

In Jou and Fischer [1982], it was shown that, in general, testing whether R is in 3NF is NP-complete.

Testing whether R is in 3NF with respect to a set of FDs F, which satisfies the intersection property, can be done in polynomial time in the size of F.

Second, if |KEYS(F)| [is greater than] 1, then the result follows, since by Lemma 42 all of the attributes A [element of] sch(R) are prime and if R is in 3NF, then it is also in 2NF.

The central part of the article gives the definitions of temporal BCNF (TBCNF) and temporal 3NF (T3NF) and algorithms for achieving TBCNF and T3NF decompositions.

Therefore we give the definition of temporal 3NF (T3NF), and present an algorithm that provides lossless, dependency-preserving, T3NF decomposition.

In the next section, we define the temporal analogue of (nontemporal) 3NF that relaxes, in a restricted way, the conditions of TBCNF to allow certain types of data redundancy in order to preserve TFDs.

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